Critical O(N) - vector nonlinear sigma - models: A resume of their field structure

Klaus Lang; Werner Ruehl

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Critical O(N) - vector nonlinear sigma - models: A resume of their field structure

Klaus Lang, Werner Ruehl

High Energy Physics - Theory · Submitted 8 Nov 1993

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It is proved that the only conserved quasi - primary currents are the energy - momentum tensor and the O(N) - Noether currents.

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arXiv IDhep-th/9311046 (version 1)

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CitationKlaus Lang, Werner Ruehl. "Critical O(N) - vector nonlinear sigma - models: A resume of their field structure." arXiv:hep-th/9311046 (1993). https://pith.science/paper/FHA52MVB

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.36 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.21 · compares with prior results 0.08 · mentions code or data availability 0.01.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

The classification of quasi - primary fields is outlined. It is proved that the only conserved quasi - primary currents are the energy - momentum tensor and the O(N) - Noether currents. Derivation of all quasi - primary fields and the resolution of degeneracy is sketched. Finally the limits d=2 and d=4 of the space dimension are discussed. Whereas the latter is trivial the former is only almost so.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The classification of quasi - primary fields is outlined.	contribution 0.96	0.73	0.07	asserted 0.95
s1	It is proved that the only conserved quasi - primary currents are the energy - momentum tensor and the O(N) - Noether currents.	result 0.99	0.85	0.63	asserted 1.00
s2	Derivation of all quasi - primary fields and the resolution of degeneracy is sketched.	contribution 0.86	0.82	0.09	asserted 0.81
s3	Finally the limits d=2 and d=4 of the space dimension are discussed.	contribution 0.96	0.81	0.04	asserted 0.92
s4	Whereas the latter is trivial the former is only almost so.	interpretation 0.72	0.43	0.05	asserted 0.98

What kind of paper the classifier reports this is: theoretical result 0.74 · evidence from proof or derivation 1.00.

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arXiv listing abstract v1

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Original abstract

The classification of quasi - primary fields is outlined. It is proved that the only conserved quasi - primary currents are the energy - momentum tensor and the O(N) - Noether currents. Derivation of all quasi - primary fields and the resolution of degeneracy is sketched. Finally the limits d=2 and d=4 of the space dimension are discussed. Whereas the latter is trivial the former is only almost so.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Conformal Bootstrap With Slightly Broken Higher Spin Symmetry
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Solving the crossing equation in the double light-cone limit yields the large-spin anomalous dimensions of higher-spin currents in theories with slightly broken higher-spin symmetry, including a prediction for the 3d ...
Convexity and Liberation at Large Spin
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Unitary conformal field theories in d>2 have an additive, convex twist spectrum at large spin, with the leading 1/s^tau_min correction fixed exactly by the lowest-twist exchanged operator.
An Algebraic Approach to the Analytic Bootstrap
hep-th 2015-10 conditional novelty 6.0 of 10

Acting with the Casimir operator on the crossing equation converts large-spin sums in conformal field theory into solvable recursion relations, reproducing known two-loop O(N) anomalous dimensions and yielding new pre...
Large spin systematics in CFT
hep-th 2015-02 conditional novelty 6.0 of 10

Conformal field theory arguments prove that the anomalous dimensions of high-spin operators contain only even powers of the inverse Casimir, extending the reciprocity principle to all loop orders and to structure constants.

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3 arXiv papers cite this in 5 sentences

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We have also checked that the results agree with known results in the large $N$ expansion [ref] .

Critical O(N) model to order $\epsilon^4$ from analytic bootstrap · Constraints from low spins · 1.00
We presented the anomalous dimension in this way to draw an analogy with equations (61) and (63) of [ref] , which give the large spin expansion of the large $N$ anomalous dimensions of non-singlet and singlet operators in the critical $O(N)$ model [ref] .

On the Higher Spin Spectrum of Chern-Simons Theory coupled to Fermions in the Large Flavour Limit · Large Spin Expansion · 1.00

Cites it as background 2 papers

Among the simplest and best known examples are the bosonic and fermionic (or Gross-Neveu) $O(N)$ vector models which are renormalizable field theories in the context of the $1/N$ expansion.[For reviews see [ref] .] These models exhibit critical behavior described by nontrivial CFTs with perturbatively calculable anomalous dimensions for all operators in their spectrum (e.g. [ref] ).

Singleton deformation of higher-spin theory and the phase structure of the three-dimensional O(N) vector model · Introduction and Summary · 1.00
(See [ref] for a review, and e.g., [ref] for calculations of scaling dimensions in vector models related to this paper) or the large flavour limit of 3d QED and QCD (e.g., [ref] ).

On the Higher Spin Spectrum of Chern-Simons Theory coupled to Fermions in the Large Flavour Limit · Introduction and Summary of Results · 0.83

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